Its a really funny thing innit?
Logically its rediculous! But then logic is cold.
I feel it would be rude to "pinch" someone else's song, and then if someone sings one I like to do then I feel a bit twitchy because then I'll feel odd about doing it myself next time - in case anyone thinks I am nicking it. Stupid!!! Luckily the sessions I go to tend not to be territorial about the songs, so its just one's own natural restraint - no glares or whispers.
I think one way around it is to make the songs your own in terms of the arrangement & performance - then they should be distinct enough from other people's versions so that you don't tread on any toes. BUT then that feeds into one of the other controversies - ie is it OK to change a song?
Hmmmmmmm.